gmac-lab-chart

READ ME

SUMMARY
This R code is used to estimate the relationship between oxygen consumption (MO2) and ambient oxygen partial pressure (PO2) in the Common galaxias (Galaxias maculatus). It is also used to estimate the critical partial pressure of oxygen for aerobic metabolism (Pcrit), which is commonly understood as the threshold below which oxygen consumption rate can no longer be sustained. The associated article is “The role of osmorespiratory compromise in hypoxia tolerance of the purportedly oxyconforming teleost Galaxias maculatus”.

AIM The article aims to test whether Galaxias maculatus can maintain oxygen consumption (MO2) as ambient PO2 falls, and if so, at what level it reaches critical partial pressure of oxygen for aerobic metabolism (Pcrit).

AUTHORS
To be added

AFFILIATIONS
To be added

AIM
To be added

Knit settings

These are the settings for the html output. We will use this to make out index file on Git

#kniter seetting
knitr::opts_chunk$set(
message = FALSE,
warning = FALSE, # no warnings
cache = TRUE,# Cacheing to save time when kniting
tidy = TRUE
)

Script contact

Jake M. Martin

Email: jake.martin@deakin.edu.au (or jake.martin.research@gmail.com)

Web: https://jake.martin.org

GitHub: https://github.com/JakeMartinResearch

Required packages

These are the R packages required for this script. You will need to install a package called pacman to run the p_load function.

# this installs and load packages
# need to install pacman
pacman::p_load("ggplot2", 
               "ggthemes", 
               "ggfortify", 
               "gtExtras", 
               "igraph",
               "dagitty",
               "ggdag",
               "ggridges",
               "gghalves",
               "ggExtra",
               "gridExtra",
               "corrplot",
               "RColorBrewer", 
               "gt", 
               "gtsummary",
               "grid",
               "plotly", # data visualisation
               
                "tidyverse", 
               "janitor", 
               "readxl", 
               "broom", 
               "data.table", 
               "devtools",
               "hms", # data tidy
               
               "marginaleffects", 
               "brms", 
               "rstan", 
               "performance", 
               "emmeans", 
               "tidybayes", 
               "vegan",
               "betareg",
               "lme4", 
               "car", 
               "lmerTest",
               "qqplotr",
               "respirometry",
               "mclust",
               # modelling 
              
               
               "datawizard", 
               "SRS" # data manipulation 
                       )

Functions (custom)

Here are some custom function used within this script.

calcSMR: authored by Chabot D. used to estimate SMR with several different methods Claireaux and Chabot (2016) DOI: doi:10.1111/jfb.12833

calcSMR = function(Y, q = c(0.1, 0.15, 0.2, 0.25, 0.3), G = 1:4) {
    u = sort(Y)
    the.Mclust <- Mclust(Y, G = G)
    cl <- the.Mclust$classification
    # sometimes, the class containing SMR is not called 1 the following
    # presumes that when class 1 contains > 10% of cases, it contains SMR,
    # otherwise we take class 2
    cl2 <- as.data.frame(table(cl))
    cl2$cl <- as.numeric(levels(cl2$cl))
    valid <- cl2$Freq >= 0.1 * length(time)
    the.cl <- min(cl2$cl[valid])
    left.distr <- Y[the.Mclust$classification == the.cl]
    mlnd = the.Mclust$parameters$mean[the.cl]
    CVmlnd = sd(left.distr)/mlnd * 100
    quant = quantile(Y, q)
    low10 = mean(u[1:10])
    low10pc = mean(u[6:(5 + round(0.1 * (length(u) - 5)))])
    # remove 5 outliers, keep lowest 10% of the rest, average Herrmann & Enders
    # 2000
    return(list(mlnd = mlnd, quant = quant, low10 = low10, low10pc = low10pc, cl = cl,
        CVmlnd = CVmlnd))
}

calcO2crit: authored by Chabot D. used to estimate O2crit (Pcript). Claireaux and Chabot (2016) DOI: doi:10.1111/jfb.12833

Note: O2 is assumed to be in percentage of dissolved oxygen (DO) to work

calcO2crit <- function(Data, SMR, lowestMO2 = NA, gapLimit = 4, max.nb.MO2.for.reg = 20) {
    # AUTHOR: Denis Chabot, Institut Maurice-Lamontagne, DFO, Canada first
    # version written in June 2009 last updated in January 2015
    method = "LS_reg"  # will become 'through_origin' if intercept is > 0
    if (is.na(lowestMO2))
        lowestMO2 = quantile(Data$MO2[Data$DO >= 80], p = 0.05)
    # Step 1: identify points where MO2 is proportional to DO
    geqSMR = Data$MO2 >= lowestMO2
    pivotDO = min(Data$DO[geqSMR])
    lethal = Data$DO < pivotDO
    N_under_SMR = sum(lethal)  # points available for regression?
    final_N_under_SMR = lethal  # some points may be removed at Step 4
    lastMO2reg = Data$MO2[Data$DO == pivotDO]  # last MO2 when regulating
    if (N_under_SMR > 1)
        theMod = lm(MO2 ~ DO, data = Data[lethal, ])
    # Step 2, add one or more point at or above SMR 2A, when there are fewer
    # than 3 valid points to calculate a regression
    if (N_under_SMR < 3) {
        missing = 3 - sum(lethal)
        not.lethal = Data$DO[geqSMR]
        DOlimit = max(sort(not.lethal)[1:missing])  # highest DO acceptable
        # to reach a N of 3
        addedPoints = Data$DO <= DOlimit
        lethal = lethal | addedPoints
        theMod = lm(MO2 ~ DO, data = Data[lethal, ])
    }
    # 2B, add pivotDO to the fit when Step 1 yielded 3 or more values?
    if (N_under_SMR >= 3) {
        lethalB = Data$DO <= pivotDO  # has one more value than 'lethal'
        regA = theMod
        regB = lm(MO2 ~ DO, data = Data[lethalB, ])
        large_slope_drop = (coef(regA)[2]/coef(regB)[2]) > 1.1  # arbitrary
        large_DO_gap = (max(Data$DO[lethalB]) - max(Data$DO[lethal])) > gapLimit
        tooSmallMO2 = lastMO2reg < SMR
        if (!large_slope_drop & !large_DO_gap & !tooSmallMO2)
            {
                lethal = lethalB
                theMod = regB
            }  # otherwise we do not accept the additional point
    }
    # Step 3 if the user wants to limit the number of points in the regression
    if (!is.na(max.nb.MO2.for.reg) & sum(lethal) > max.nb.MO2.for.reg) {
        Ranks = rank(Data$DO)
        lethal = Ranks <= max.nb.MO2.for.reg
        theMod = lm(MO2 ~ DO, data = Data[lethal, ])
        final_N_under_SMR = max.nb.MO2.for.reg
    }
    # Step 4
    predMO2 = as.numeric(predict(theMod, data.frame(DO = Data$DO)))
    Data$delta = (Data$MO2 - predMO2)/predMO2 * 100  # residuals set to zero
    # when below pivotDO
    Data$delta[Data$DO < pivotDO | lethal] = 0
    tol = 0  # any positive residual is unacceptable
    HighValues = Data$delta > tol
    Ranks = rank(-1 * Data$delta)
    HighMO2 = HighValues & Ranks == min(Ranks)  # keep largest residual
    if (sum(HighValues) > 0)
        {
            nblethal = sum(lethal)
            Data$W = NA
            Data$W[lethal] = 1/nblethal
            Data$W[HighMO2] = 1
            theMod = lm(MO2 ~ DO, weight = W, data = Data[lethal | HighMO2, ])
            # This new regression is always an improvement, but there can still
            # be points above the line, so we repeat
            predMO2_2 = as.numeric(predict(theMod, data.frame(DO = Data$DO)))
            Data$delta2 = (Data$MO2 - predMO2_2)/predMO2_2 * 100
            Data$delta2[Data$DO < pivotDO] = 0
            tol = Data$delta2[HighMO2]
            HighValues2 = Data$delta2 > tol
            if (sum(HighValues2) > 0)
                {
                  Ranks2 = rank(-1 * Data$delta2)
                  HighMO2_2 = HighValues2 & Ranks2 == 1  # keep the largest residual
                  nblethal = sum(lethal)
                  Data$W = NA
                  Data$W[lethal] = 1/nblethal
                  Data$W[HighMO2_2] = 1
                  theMod2 = lm(MO2 ~ DO, weight = W, data = Data[lethal | HighMO2_2,
                    ])
                  # is new slope steeper than the old one?
                  if (theMod2$coef[2] > theMod$coef[2]) {
                    theMod = theMod2
                    HighMO2 = HighMO2_2
                  }
                }  # end second search for high value
        }  # end first search for high value
    Coef = coefficients(theMod)
    # Step 5, check for positive intercept
    AboveOrigin = Coef[1] > 0
    # if it is, we use a regression that goes through the origin
    if (AboveOrigin) {
        theMod = lm(MO2 ~ DO - 1, data = Data[lethal, ])
        Coef = c(0, coefficients(theMod))  # need to add the intercept (0)
        # manually to have a pair of coefficients
        method = "through_origin"
        HighMO2 = rep(FALSE, nrow(Data))  # did not use the additional value
        # from Step 4
    }
    po2crit = as.numeric(round((SMR - Coef[1])/Coef[2], 1))
    sum_mod = summary(theMod)
    anov_mod = anova(theMod)
    O2CRIT = list(o2crit = po2crit, SMR = SMR, Nb_MO2_conforming = N_under_SMR, Nb_MO2_conf_used = final_N_under_SMR,
        High_MO2_required = sum(HighMO2) == 1, origData = Data, Method = method,
        mod = theMod, r2 = sum_mod$r.squared, P = anov_mod$"Pr(>F)", lethalPoints = which(lethal),
        AddedPoints = which(HighMO2))
}  # end function

plotO2crit: used to plot the modes used for the calcO2crit function. Claireaux and Chabot (2016) DOI: doi:10.1111/jfb.12833

plotO2crit <- function(o2critobj, plotID = "", Xlab = "Dissolved oxygen (% sat.)",
    Ylab = "dotitalumol", smr.cex = 0.9, o2crit.cex = 0.9, plotID.cex = 1.2, Transparency = T,
    ...) {
    # AUTHOR: Denis Chabot, Institut Maurice-Lamontagne, DFO, Canada first
    # version written in June 2009 last updated 2015-02-09 for R plotting
    # devices that do not support transparency (e.g., postscript), set
    # Transparency to FALSE
    smr = o2critobj$SMR
    if (Ylab %in% c("dotitalumol", "italumol", "dotumol", "umol", "dotitalmg", "italmg",
        "dotmg", "mg")) {
        switch(Ylab, dotitalumol = {
            mo2.lab = expression(paste(italic(dot(M))[O[2]], " (", mu, "mol ", O[2],
                " ", min^-1, " ", kg^-1, ")"))
        }, italumol = {
            mo2.lab = expression(paste(italic(M)[O[2]], " (", mu, "mol ", O[2], " ",
                min^-1, " ", kg^-1, ")"))
        }, dotumol = {
            mo2.lab = expression(paste(dot(M)[O[2]], " (", mu, "mol ", O[2], " ",
                min^-1, " ", kg^-1, ")"))
        }, umol = {
            mo2.lab = expression(paste(M[O[2]], " (", mu, "mol ", O[2], " ", min^-1,
                " ", kg^-1, ")"))
        }, dotitalmg = {
            mo2.lab = expression(paste(italic(dot(M))[O[2]], " (mg ", O[2], " ",
                h^-1, " ", kg^-1, ")"))
        }, italmg = {
            mo2.lab = expression(paste(italic(M)[O[2]], " (mg ", O[2], " ", h^-1,
                " ", kg^-1, ")"))
        }, dotmg = {
            mo2.lab = expression(paste(dot(M)[O[2]], " (mg ", O[2], " ", h^-1, " ",
                kg^-1, ")"))
        }, mg = {
            mo2.lab = expression(paste(M[O[2]], " (mg ", O[2], " ", h^-1, " ", kg^-1,
                ")"))
        })
    } else mo2.lab = Ylab
    if (Transparency) {
        Col = c(rgb(0, 0, 0, 0.7), "red", "orange")
    } else {
        Col = c(grey(0.3), "red", "orange")
    }
    Data = o2critobj$origData
    lowestMO2 = quantile(Data$MO2[Data$DO >= 80], p = 0.05)  # I added this
    Data$Color = Col[1]
    Data$Color[o2critobj$lethalPoints] = Col[2]
    Data$Color[o2critobj$AddedPoints] = Col[3]
    # ordinary LS regression without added points: blue line, red symbols
    # ordinary LS regression with added points: blue line, red & orange symbols
    # regression through origin: green dotted line, red symbols
    line.color = ifelse(o2critobj$Method == "LS_reg", "blue", "darkgreen")
    line.type = ifelse(o2critobj$Method == "LS_reg", 1, 3)
    limX = c(0, max(Data$DO))
    limY = c(0, max(Data$MO2))
    plot(MO2 ~ DO, data = Data, xlim = limX, ylim = limY, col = Data$Color, xlab = Xlab,
        ylab = mo2.lab, ...)
    coord <- par("usr")
    if (plotID != "") {
        text(0, coord[4], plotID, cex = plotID.cex, adj = c(0, 1.2))
    }
    abline(h = lowestMO2, col = "pink")  # I added this
    abline(h = smr, col = "orange")
    text(coord[1], smr, "SMR", adj = c(-0.1, 1.3), cex = smr.cex)
    text(coord[1], smr, round(smr, 1), adj = c(-0.1, -0.3), cex = smr.cex)
    if (!is.na(o2critobj$o2crit)) {
        abline(o2critobj$mod, col = line.color, lty = line.type)
        segments(o2critobj$o2crit, smr, o2critobj$o2crit, coord[3], col = line.color,
            lwd = 1)
        text(x = o2critobj$o2crit, y = 0, o2critobj$o2crit, col = line.color, cex = o2crit.cex,
            adj = c(-0.1, 0.5))
    }
}  # end of function

Working directories

Input

meta_files_wd: Directory for the metadata

wd <- getwd()
meta_files_wd <- paste0(wd, "./meta-data")  # creates a variable with the name of the wd we want to use

labchart_wd: Directory for Labchart estimated slopes

labchart_wd <- paste0(wd, "./lab-chart-slopes")

Output

output_fig_wd: this is where we will put the figures

output_fig_wd <- paste0(wd, "./output-fig")
ifelse(!dir.exists("output-fig"), dir.create("output-fig"), "Folder already exists")

## [1] "Folder already exists"

Input files

Slopes (MO2)

labchart_df: We have imported the slopes extracted in LabChart during each phase of the experiment

 setwd(labchart_wd)
# 
# # Get the names of all sheets in the Excel file
sheet_names <- excel_sheets("labchart-all-dates_v2.xlsx")
all_trials_select <- c("start_date", "order", "phase", "cycle", "date", "time")
labchart_list <- list()

for (sheet in sheet_names) {

  df <- read_excel("labchart-all-dates_v2.xlsx", sheet = sheet) %>% 
  dplyr::rename_with(tolower)
  
a_name <- paste0("a_", tolower(sheet))
a_df <- df %>%
  dplyr::select(starts_with('a'), all_trials_select) %>% 
  dplyr::rename(temp = a_temp) %>% 
  dplyr::mutate(across(starts_with('a'), as.numeric)) %>% 
  pivot_longer(
    cols = starts_with('a'), # Select all columns to pivot
    names_to = c("chamber_id", ".value"), # Separate column names into 'id' and other variables
    names_sep = "_"
  ) %>%
  dplyr::mutate(respirometer_group = "a") # Add a new column with a fixed value

labchart_list[[a_name]]<- a_df

b_name <- paste0("b_", tolower(sheet))
b_df <- df %>% 
  dplyr::select(starts_with('b'), all_trials_select) %>% 
  dplyr::rename(temp = b_temp) %>% 
  dplyr::mutate(across(starts_with('b'), as.numeric)) %>% 
  pivot_longer(
    cols = starts_with('b'), # Select all columns to pivot
    names_to = c("chamber_id", ".value"), # Separate column names into 'id' and other variables
    names_sep = "_"
  ) %>% 
    dplyr::mutate(respirometer_group = "b")

labchart_list[[b_name]] <- b_df

c_name <- paste0("c_", tolower(sheet))
c_df <- df %>% 
  dplyr::select(starts_with('c'), all_trials_select) %>% 
  dplyr::rename(temp = c_temp,
                i_cycle = cycle) %>% 
  dplyr::mutate(across(starts_with('c'), as.numeric)) %>%
  pivot_longer(
    cols = starts_with('c'), # Select all columns to pivot
    names_to = c("chamber_id", ".value"), # Separate column names into 'id' and other variables
    names_sep = "_"
  ) %>% 
    dplyr::mutate(respirometer_group = "c") %>% 
  dplyr::rename(cycle = i_cycle)

labchart_list[[c_name]] <- c_df

d_name <- paste0("d_", tolower(sheet))
d_df <- df %>% 
  dplyr::select(starts_with('d'), all_trials_select) %>% 
  dplyr::rename(temp = d_temp,
                i_date = date) %>% 
  dplyr::mutate(across(starts_with('d'), as.numeric)) %>%
  pivot_longer(
    cols = starts_with('d'), # Select all columns to pivot
    names_to = c("chamber_id", ".value"), # Separate column names into 'id' and other variables
    names_sep = "_"
  ) %>% 
    dplyr::mutate(respirometer_group = "d") %>% 
  dplyr::rename(date = i_date)

labchart_list[[d_name]] <- d_df
}


labchart_df <- bind_rows(labchart_list) %>% 
  dplyr::mutate(resp_cat_date = paste0(respirometer_group, "_", start_date),
                chamber_n = str_extract(chamber_id, "\\d+"),
                id_prox = paste0(resp_cat_date, "_", chamber_n),
                time_hms = as_hms(time*3600),
                date_chr = format(date, "%d/%m/%Y")
                )

Metadata

metadata: This is the meta data for each chamber

Note: We are also adding volume based on chamber type.

setwd(meta_files_wd)

metadata <- read_excel("Morpho.xlsx", na = "NA") %>%
    dplyr::mutate(id_split = id) %>%
    tidyr::separate(id_split, into = c("respirometer_group", "salinity_group", "start_date",
        "chamber"), sep = "_") %>%
    dplyr::mutate(volume = dplyr::case_when(chamber_type == "L" ~ 0.3, chamber_type ==
        "M_M" ~ 0.105, chamber_type == "M_NM" ~ 0.11, chamber_type == "S" ~ 0.058,
        chamber_type == "SM" ~ 0.075, chamber_type == "D3" ~ 0.055, TRUE ~ NA), id_prox = paste0(respirometer_group,
        "_", start_date, "_", chamber))

Combinding metadata

Adding the meta data to LabChart slopes

labchart_tidy <- labchart_df %>%
    dplyr::select(-start_date, -respirometer_group) %>%
    left_join(metadata, by = "id_prox") %>%
    dplyr::arrange(id)

Data

Numbers

We have 64 fish with MO2 data

n <- labchart_tidy %>%
    dplyr::filter(chamber_condition == "fish") %>%
    dplyr::distinct(id) %>%
    nrow(.)

paste0("n = ", n)

## [1] "n = 64"

labchart_tidy %>%
    dplyr::group_by(salinity_group) %>%
    dplyr::reframe(`n total` = length(unique(id))) %>%
    gt() %>%
    cols_label(salinity_group = "Salinity group") %>%
    cols_align(align = "center", columns = everything())

Salinity group	n total
0	48
9	48

Size

Here we caculate the mean length and size of fish used in the experiment.

mass_length <- labchart_tidy %>%
    dplyr::group_by(id) %>%
    dplyr::sample_n(1) %>%
    dplyr::ungroup() %>%
    dplyr::reframe(x_mass = round(mean(mass), 3), min_mass = round(min(mass), 3),
        max_mass = round(max(mass), 3), x_length = round(mean(length), 2), min_length = round(min(length),
            2), max_length = round(max(length), 2))

mass_mean <- mass_length %>%
    pull(x_mass)

mass_min <- mass_length %>%
    pull(min_mass)

mass_max <- mass_length %>%
    pull(max_mass)

length_mean <- mass_length %>%
    pull(x_length)

length_min <- mass_length %>%
    pull(min_length)

length_max <- mass_length %>%
    pull(max_length)

paste0("The mean mass of fish was ", mass_mean, " g (range: ", mass_min, "–", mass_max,
    ")", ", and the mean length was ", length_mean, " mm (range: ", length_min, "–",
    length_max, ")")

## [1] "The mean mass of fish was NA g (range: NA–NA), and the mean length was NA mm (range: NA–NA)"

Filtering trials

We will remove 6 trials which had errors. These are as follows:

• a_0_25nov_3 needs to be removed (fish died)
• b_0_26nov_4 flat lined early
• c_0_22nov_2 accidentally opened the chamber early
• c_9_26nov_2 stopped trial early, took too long
• c_9_26nov_4 stopped trial early, took too long
• d_9_27nov_3 sensor was jumpy and end points were hard to confidently ID visually
  

remove_trial_error <- c("a_0_25nov_3", "b_0_26nov_4", "c_0_22nov_2", "c_9_26nov_2",
    "c_9_26nov_4", "d_9_27nov_3")

labchart_tidy <- labchart_tidy %>%
    dplyr::filter(!(id %in% remove_trial_error))

Filtering MO2 estimates

Here we apply the following filters to the MO2 data:

• Remove the first 5 SMR cycles (burn in)
• Remove all positive raw slopes
• Remove all MO2 calculated using less then 60 data points (5 min)
• Remove all MO2 calculated if o2 increases in a closed phase (i.e. trial has ended)
  

cycle_burn <- 0:4

labchart_tidy <- labchart_tidy %>%
    dplyr::filter(!(cycle %in% cycle_burn) & mo2corr < 0 & n > 60 & chamber_condition ==
        "fish")

# Now we remove the points after the chamber is opened This is a function to do
# so
filter_o2_increase <- function(group) {
    group <- group %>%
        mutate(o2_diff = o2 - lag(o2))  # Calculate the difference in 'o2'

    # Find the first index where 'o2_diff' exceeds 1
    cutoff_index <- which(group$o2_diff > 1)[1]

    # Filter the data up to the cutoff index, or return the full group if no
    # cutoff
    if (!is.na(cutoff_index)) {
        group <- group[1:(cutoff_index - 1), ]
    }

    return(group)
}

# Apply the function to each group of 'chamber_id'
labchart_tidy_fish_closed <- labchart_tidy %>%
    dplyr::filter(phase != "smr") %>%
    group_by(id) %>%
    group_split() %>%
    lapply(filter_o2_increase) %>%
    bind_rows() %>%
    select(-o2_diff)

labchart_tidy_fish_smr <- labchart_tidy %>%
    dplyr::filter(phase == "smr")

labchart_tidy_fish <- rbind(labchart_tidy_fish_smr, labchart_tidy_fish_closed) %>%
    dplyr::arrange(id, order)

Calculating SMR

We have estimated SMR with two different appraches.

First using the mean of the lowest 3 values (smr_3l_means)

smr_3l_means <- labchart_tidy_fish %>%
  dplyr::group_by(id) %>% 
  dplyr::filter(phase == "smr") %>%
  dplyr::arrange(desc(mo2corr)) %>%
  dplyr::slice_head(n = 3)  %>% # Select the three lowest MO2
  dplyr::ungroup() %>% 
  dplyr::group_by(id) %>% 
  dplyr::reframe(smr_l3 = mean(mo2corr))

# Combine the processed "smr" phase with all other phases
labchart_tidy_fish <- labchart_tidy_fish %>%
  dplyr::left_join(., smr_3l_means, by = "id")

Second using the calcSMR function by Chabot, Steffensen and Farrell (2016) DOI: 10.1111/jfb.12845. Specifically, We use mean of the lowest normal distribution (MLND) where CVmlnd < 5.4 and the mean of the lower 20% quantile (q0.2) were CVmlnd > 5.4. If CVmlnd is not calculated we have used q0.2.

labchart_chabot_smr <- labchart_tidy_fish %>%
    dplyr::filter(phase == "smr")

# Extract distinct IDs
ids <- labchart_chabot_smr %>%
    dplyr::distinct(id) %>%
    dplyr::pull()

# Initialise an empty list to store SMR data
smr_list <- list()

# Process each ID
for (id_i in ids) {
    tryCatch({
        # Filter the data for the current ID
        df_i <- labchart_chabot_smr %>%
            dplyr::filter(id == id_i) %>%
            dplyr::mutate(abs_mo2corr = abs(mo2corr))

        # Calculate SMR results
        calcSMR_results <- calcSMR(df_i$abs_mo2corr)
        CVmlnd_i <- calcSMR_results$CVmlnd
        quant_i <- calcSMR_results$quant %>%
            as_tibble()
        quant_20per_i <- quant_i$value[3]
        mlnd_i <- calcSMR_results$mlnd
        smr_value <- if_else(CVmlnd_i < 5.4, mlnd_i, quant_20per_i)
        smr_type <- if_else(CVmlnd_i < 5.4, "mlnd", "quant_20per")
        smr_value <- if_else(is.na(smr_value), quant_20per_i, smr_value)
        smr_type <- if_else(is.na(smr_type), "quant_20per", smr_type)

        # Create a data frame for the current ID
        smr_df <- tibble(id = id_i, smr = smr_value, smr_est = smr_type)

    }, error = function(e) {
        # Handle errors by assigning NA values
        smr_df <- tibble(id = id_i, smr = NA, smr_est = NA)
    })

    # Append to the list
    smr_list[[id_i]] <- smr_df
}

# Combine all individual SMR data frames into one
smr_df <- bind_rows(smr_list) %>%
    dplyr::rename(smr_chabot = smr, smr_chabot_method = smr_est)

labchart_tidy_fish <- labchart_tidy_fish %>%
    dplyr::left_join(., smr_df, by = "id")

Transforming MO2

Here we are transforming the MO2 units. The resulting vaules are as follows:

• MO2 = absolute value of the background and leak corrected mo2 slope from Labchart (mo2corr) times the net volume of the chamber (volume - fish mass), times 60, times 60, to achieve mg O2 / h.
• MO2_g = MO2 divided by fish mass to achieve mg O2 / g/ h (i.e. mass standardised)
• SMR = absolute value of the mean of the three lowest MO2 during the SMR phase (smr_l3) times the net volume of the chamber (volume - fish mass), times 60, times 60, to achieve mg MO2 / h
• SMR_g = SMR divided by fish mass
• SMR_CHABOT = absolute value of the SMR estimates using methods descibed by Chabot, Steffensen and Farrell (2016) (smr_chabot)
• SMR_g = SMR_CHABOT divided by fish mass
• DO = dissolved oxygen percentage calculated from o2 values (mg/L) using the recorded temperature, salinity, and a constant atmospheric pressure (1013.25)

# Combine back into one data frame
labchart_tidy_fish <- labchart_tidy_fish %>% 
    dplyr::mutate(DO = conv_o2(
                   o2 = o2,
                   from = "mg_per_l",
                   to = "percent_a.s.",
                   temp = temp, #C
                   sal = measured_salinity,
                   atm_pres = 1013.25),
                  net_volume = volume - mass/1000,
                  MO2 = abs(mo2corr)*net_volume*60*60,
                  MO2_g = MO2/mass,
                  SMR = abs(smr_l3)*net_volume*60*60,
                  SMR_g = SMR/mass,
                  SMR_CHABOT = abs(smr_chabot)*net_volume*60*60,
                  SMR_CHABOT_g = SMR_CHABOT/mass
                  )

Visualise

Here we plot all oxygen consumption (MO2; mg O2/g/h) by dissolved oxygen percentage (DO) for all fish, including all SMR estimates.

labchart_tidy_fish %>% 
  ggplot(aes(y = MO2_g, x = DO, colour = id)) + # Default aesthetics
  geom_point(show.legend = FALSE) +
  geom_smooth(aes(group = id), method = "lm", se = FALSE, colour = scales::alpha("black", 0.5)) + # Transparent black lines
  geom_smooth(method = "lm", se = TRUE, colour = "red") + # Overall smooth line
  geom_smooth(se = TRUE, colour = "red", linetype = "dashed") +
  theme_clean() +
  labs(
    subtitle = "All values",
    x = "Dissolved oxygen percentage (DO)",
    y = "MO2 (mg O2 g/h)"
  )

Same plot but without SMR values.

labchart_tidy_fish %>% 
  dplyr::filter(phase != "smr") %>% 
  ggplot(aes(y = MO2_g, x = DO, colour = id)) + # Default aesthetics
  geom_point(show.legend = FALSE) +
  geom_smooth(aes(group = id), method = "lm", se = FALSE, colour = scales::alpha("black", 0.5)) + # Transparent black lines
  geom_smooth(method = "lm", se = TRUE, colour = "red") + # Overall smooth line
  geom_smooth(se = TRUE, colour = "red", linetype = "dashed") +
  theme_clean() +
  labs(
    subtitle = "Only closed periods",
    x = "Dissolved oxygen percentage (DO)",
    y = "MO2 (O2 mg/g/h)"
  )

Looking at the difference responses in the two salinity groups. It’s appears more variable in freshwater.

labchart_tidy_fish %>% 
  ggplot(aes(y = MO2_g, x = DO, colour = id)) + # Default aesthetics
  geom_point(show.legend = FALSE) +
  geom_smooth(aes(group = id), method = "lm", se = FALSE, colour = scales::alpha("black", 0.5)) + # Transparent black lines
  geom_smooth(method = "lm", se = TRUE, colour = "red") + # Overall smooth line
  geom_smooth(se = TRUE, colour = "red", linetype = "dashed") +
  theme_clean() +
  facet_wrap(~salinity_group) +
  labs(
    subtitle = "mo2 vs o2 by salinity treatment",
    x = "Dissolved oxygen percentage (DO)",
    y = "MO2 (O2 mg/g/h)"
  )

Looking at the difference chamber types

labchart_tidy_fish %>% 
  ggplot(aes(y = MO2_g, x = DO, colour = id)) + # Default aesthetics
  geom_point(show.legend = FALSE) +
  geom_smooth(aes(group = id), method = "lm", se = FALSE, colour = scales::alpha("black", 0.5)) + # Transparent black lines
  geom_smooth(method = "lm", se = TRUE, colour = "red") + # Overall smooth line
  geom_smooth(se = TRUE, colour = "red", linetype = "dashed") +
  theme_clean() +
  facet_wrap(~chamber_type, scale = "free") +
  labs(
    subtitle = "mo2 vs o2 by chamber type",
    x = "Dissolved oxygen percentage (DO)",
    y = "MO2 (O2 mg/g/h)"
  )

Recreating Urbina et al. (2012)

min_o2 <- min(labchart_tidy_fish$o2, na.rm = TRUE)
max_o2 <- max(labchart_tidy_fish$o2, na.rm = TRUE)

labchart_tidy_fish <- labchart_tidy_fish %>%
  mutate(o2_group = cut(o2, 
                        breaks = seq(min_o2, max_o2, length.out = 11), # 12 intervals, so 13 breakpoints
                        labels = paste0("Group ", 1:10), 
                        include.lowest = TRUE))

time_bin_df <- labchart_tidy_fish %>% 
  dplyr::group_by(o2_group) %>% 
  dplyr::reframe(mean_MO2_g = mean(MO2_g)*31.25,
                 mean_o2 = mean(o2),
                 n = length(MO2_g)*31.25,
                 MO2_g_sd = sd(MO2_g)*31.25,
                 o2_sd = sd(o2))

time_bin_df %>% 
  ggplot(aes(y = mean_MO2_g, x = mean_o2)) +
  # Add raw data points
  geom_point(data = labchart_tidy_fish, aes(y = MO2_g*31.25, x = o2), 
             size = 2, color = "grey", alpha = 0.5) +  # Raw data points
  # Add summary points
  geom_point(size = 3, colour = "black", show.legend = FALSE) +
  # Add vertical error bars
  geom_errorbar(aes(ymin = mean_MO2_g - MO2_g_sd, ymax = mean_MO2_g + MO2_g_sd), 
                width = 0.15, colour = "black") +
  # Add horizontal error bars
  geom_errorbarh(aes(xmin = mean_o2 - o2_sd, xmax = mean_o2 + o2_sd), 
                 height = 0.005, colour = "black") +
  theme_clean() +
  labs(
    subtitle = "All values with error bars",
    x = "O2 (mg/L)",
    y = "MO2 (umol O2 g/h)"
  )

Plotting SMR

Plotting MO2 estimates for each fish. The dashed red line is Chabot SMR methods, and the solid line is the mean of the lowest 3 measures (excluding the first 5 cycles)

Notes: There’s something wired going on with a_0_25nov_2 it seems like many of the raw MO2 values are positive.

# Create output directory if needed
output_fig_slopes_wd <- file.path(output_fig_wd, "slopes")
if (!dir.exists(output_fig_slopes_wd)) {
    dir.create(output_fig_slopes_wd)
}

ids <- labchart_tidy_fish %>%
    dplyr::distinct(id) %>%
    pull(id) %>%
    as.list()

MO2_plot_list <- list()

# 1) Open the PDF device once
pdf(file = file.path(output_fig_slopes_wd, "combined_slopes.pdf"), width = 8, height = 6)

# 2) Loop over IDs and create each plot
for (id_i in ids) {

    smr_chabot <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i) %>%
        dplyr::slice(1) %>%
        dplyr::pull(SMR_CHABOT)

    smr_l3 <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i) %>%
        dplyr::slice(1) %>%
        dplyr::pull(SMR)

    plot <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i) %>%
        ggplot(aes(x = o2, y = MO2)) + geom_hline(yintercept = smr_chabot, linetype = "dashed",
        color = "darkred") + geom_hline(yintercept = smr_l3, color = "darkred") +
        geom_point(aes(colour = phase)) + theme_clean() + labs(subtitle = paste0(id_i,
        " slopes"), x = "Mean o2 (mg_per_l)", y = "abs(mo2) (mg_per_l)")

    # Instead of saving each plot separately, just print it
    print(plot)

    MO2_plot_list[[id_i]] <- plot
}

# 3) Close the PDF device *after* the loop
dev.off()

## png 
##   2

for (p in MO2_plot_list) {
    print(p)
}

Analysis

Incremental regression analyses

Here we are following the methods Urbina et al. (2012) with an incremental regression analyses, in order to determine the best fit for the data.

This analysis evaluated each polynomial order equation starting at zero and then increasing to the third order. This permitted a mathematical assessment of whether the data best fitted a single linear relationship (i.e. the fish were oxyconforming), or whether a PO2 crit value could be determined as the intersection point of two distinct linear relationships (one at hypoxic oxygen concentrations, the other at normoxic; i.e. oxyregulation). This analysis evaluated each polynomial order equation starting at zero and then increasing to the third order. This permitted a mathematical assessment of whether the data best fitted a single linear relationship (i.e. the fish were oxyconforming), or whether a PO2 crit value could be determined as the intersection point of two distinct linear relationships (one at hypoxic oxygen concentrations, the other at normoxic; i.e. oxyregulation).

No SMR

I have not included MO2 values calculated during the SMR phase of the experiment, as I was concerned the the high density region would effluence the regression. Specifically, a high density of points at high o2 values could lead to overfitting in that region, while underfitting or misrepresenting trends in lower-density regions (e.g., low o2).

ids <- labchart_tidy_fish %>% 
  dplyr::distinct(id) %>% 
  pull(id) %>% 
  as.list()

model_comparison_list <- list()

for (id_i in ids) {

df_i <- labchart_tidy_fish %>% 
  dplyr::filter(phase != "smr", id == id_i)

models <- list(
  lm_0 = lm(MO2 ~ 1, data = df_i),                # 0th-order (constant mean)
  lm_1 = lm(MO2 ~ o2, data = df_i),               # 1st-order (linear)
  lm_2 = lm(MO2 ~ poly(o2, 2), data = df_i),      # 2nd-order (quadratic)
  lm_3 = lm(MO2 ~ poly(o2, 3), data = df_i)       # 3rd-order (cubic)
)

# Extract metrics to compare models
model_comparison_list[[id_i]] <- purrr::map_df(models, glance, .id = "model") %>% 
  dplyr::mutate(id = id_i) %>% 
  dplyr::select(id, everything())

}

model_comparison <- bind_rows(model_comparison_list) %>% 
  dplyr::mutate(poly = as.numeric(str_remove_all(model, "lm_")))

model_comparison

## # A tibble: 256 × 15
##    id       model r.squared adj.r.squared  sigma statistic  p.value    df logLik
##    <chr>    <chr>     <dbl>         <dbl>  <dbl>     <dbl>    <dbl> <dbl>  <dbl>
##  1 a_0_24n… lm_0    0              0      0.0162   NA      NA          NA   49.1
##  2 a_0_24n… lm_1    0.400          0.363  0.0130   10.7     0.00484     1   53.7
##  3 a_0_24n… lm_2    0.476          0.406  0.0125    6.81    0.00785     2   55.0
##  4 a_0_24n… lm_3    0.560          0.465  0.0119    5.93    0.00788     3   56.5
##  5 a_0_24n… lm_0    0              0      0.0299   NA      NA          NA   42.4
##  6 a_0_24n… lm_1    0.00397       -0.0514 0.0306    0.0718  0.792       1   42.4
##  7 a_0_24n… lm_2    0.230          0.139  0.0277    2.53    0.109       2   45.0
##  8 a_0_24n… lm_3    0.544          0.459  0.0220    6.37    0.00477     3   50.2
##  9 a_0_24n… lm_0    0              0      0.0189   NA      NA          NA   46.5
## 10 a_0_24n… lm_1    0.460          0.426  0.0143   13.6     0.00197     1   52.0
## # ℹ 246 more rows
## # ℹ 6 more variables: AIC <dbl>, BIC <dbl>, deviance <dbl>, df.residual <int>,
## #   nobs <int>, poly <dbl>

Now we are selecting the best fitting model for each fish. Most often the best fitting model is a 0th-order polynomial (n = 36, 62.07%), suggesting that MO2 does not show a statistically significant dependence on the o2. In other words, the metabolic rate does not adjust based on oxygen availability, and there is no clear critical oxygen threshold (Pcrit) where the relationship changes. This is indicative of a oxyregulator.

The next most common is a 3rd-order polynomial (n = 16, 27.59%) which may suggest the presences of some kind of oxygen threshold where the relationship changes.

Only five fish (8.62%) appear to have a linear relationship (1st-order polynomial) which would be expected for oxyconformers.

best_model <- model_comparison %>%
    dplyr::group_by(id) %>%
    dplyr::arrange(desc(AIC)) %>%
    dplyr::slice(1) %>%
    dplyr::ungroup()

total_fish <- nrow(best_model)

model_summary <- best_model %>%
    dplyr::group_by(poly) %>%
    dplyr::reframe(n = length(id), percent = round((n/total_fish) * 100, 2))

model_summary

## # A tibble: 4 × 3
##    poly     n percent
##   <dbl> <int>   <dbl>
## 1     0    33   51.6 
## 2     1    10   15.6 
## 3     2     5    7.81
## 4     3    16   25

Visualising the regressions

ids <- labchart_tidy_fish %>%
    dplyr::distinct(id) %>%
    pull(id) %>%
    as.list()

model_comparison_plot <- list()

for (id_i in ids) {

    poly_i <- best_model %>%
        dplyr::filter(id == id_i) %>%
        dplyr::pull(poly)

    poly_i_name <- best_model %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(name = case_when(poly == 0 ~ "0th-order polynomial", poly ==
            1 ~ "1st-order polynomial", poly == 2 ~ "2nd-order polynomial", poly ==
            3 ~ "3rd-order polynomial", TRUE ~ "ERROR")) %>%
        dplyr::pull(name)

    r <- best_model %>%
        dplyr::filter(id == id_i) %>%
        dplyr::pull(r.squared) %>%
        round(., 2)

    sigma <- best_model %>%
        dplyr::filter(id == id_i) %>%
        dplyr::pull(sigma) %>%
        round(., 2)

    mean_MO2 <- labchart_tidy_fish %>%
        dplyr::filter(phase != "smr" & id == id_i) %>%
        dplyr::reframe(mean = mean(MO2), na.rm = TRUE) %>%
        dplyr::pull(mean)

    x_max <- labchart_tidy_fish %>%
        dplyr::filter(phase != "smr" & id == id_i) %>%
        dplyr::reframe(max = max(o2), na.rm = TRUE) %>%
        dplyr::pull(max)

    y_max <- labchart_tidy_fish %>%
        dplyr::filter(phase != "smr" & id == id_i) %>%
        dplyr::reframe(max = max(MO2), na.rm = TRUE) %>%
        dplyr::pull(max)

    plot <- labchart_tidy_fish %>%
        dplyr::filter(phase != "smr" & id == id_i) %>%
        ggplot(aes(x = o2, y = MO2)) + geom_point() + geom_smooth(method = "lm",
        formula = y ~ poly(x, poly_i), se = FALSE, colour = "blue") + geom_hline(yintercept = mean_MO2,
        colour = "grey", linetype = "dashed", linewidth = 1) + annotate("text", x = x_max/2,
        y = y_max, label = paste0(poly_i_name, "\n", "R = ", r, " Sigma = ", sigma),
        hjust = 0, vjust = 1, size = 4) + labs(title = paste0(id_i), x = "O2 (mg/L)",
        y = "MO2 (mg O2 g/h)") + theme_minimal()

    print(plot)
}

Weighted regression

Here we are doing the same as above but weighting the importance of each data point in fitting the model. Points with higher weights influence the model fit more, while points with lower weights have less impact. We are making sure that High-density regions (e.g. SMR vaules) have lower weights to reduce their over-representation.

This is achieved by dividing the o2 values into bins, computing the frequency of points in each bin, and assigning weights as the inverse of frequency for each point.

ids <- labchart_tidy_fish %>%
  dplyr::distinct(id) %>%
  pull(id) %>%
  as.list()

weighted_model_comparison_list <- list()

for (id_i in ids) {
  
  # Filter data for the current ID
  df_i <- labchart_tidy_fish %>%
    dplyr::filter(id == id_i)
  
  # Calculate weights based on O2 density
  df_i <- df_i %>%
    dplyr::mutate(
      o2_bin = cut(o2, breaks = 10),  # Divide O2 into 10 bins
      bin_freq = dplyr::n(),          # Count points in each bin
      weight = 1 / bin_freq           # Weight = inverse frequency
    )
  
  # Fit models with weights
  models <- list(
    lm_0 = lm(MO2 ~ 1, data = df_i, weights = weight),                # 0th-order (constant mean)
    lm_1 = lm(MO2 ~ o2, data = df_i, weights = weight),               # 1st-order (linear)
    lm_2 = lm(MO2 ~ poly(o2, 2), data = df_i, weights = weight),      # 2nd-order (quadratic)
    lm_3 = lm(MO2 ~ poly(o2, 3), data = df_i, weights = weight)       # 3rd-order (cubic)
  )
  
  # Extract metrics to compare models
  weighted_model_comparison_list[[id_i]] <- purrr::map_df(models, glance, .id = "model") %>%
    dplyr::mutate(id = id_i) %>%
    dplyr::select(id, everything())
}

# Combine results into a single data frame
weighted_model_comparison <- bind_rows(weighted_model_comparison_list) %>%
  dplyr::mutate(poly = as.numeric(stringr::str_remove_all(model, "lm_")))

weighted_model_comparison

## # A tibble: 256 × 15
##    id      model r.squared adj.r.squared   sigma statistic  p.value    df logLik
##    <chr>   <chr>     <dbl>         <dbl>   <dbl>     <dbl>    <dbl> <dbl>  <dbl>
##  1 a_0_24… lm_0    0             0       0.00587    NA     NA          NA   76.8
##  2 a_0_24… lm_1    0.00610      -0.0194  0.00593     0.239  0.628       1   77.0
##  3 a_0_24… lm_2    0.0430       -0.00736 0.00589     0.854  0.434       2   77.8
##  4 a_0_24… lm_3    0.0518       -0.0250  0.00594     0.674  0.573       3   77.9
##  5 a_0_24… lm_0    0             0       0.00662    NA     NA          NA   74.4
##  6 a_0_24… lm_1    0.0399        0.0164  0.00657     1.70   0.199       1   75.2
##  7 a_0_24… lm_2    0.0599        0.0129  0.00658     1.28   0.290       2   75.7
##  8 a_0_24… lm_3    0.0685       -0.00319 0.00663     0.956  0.423       3   75.9
##  9 a_0_24… lm_0    0             0       0.00546    NA     NA          NA   79.9
## 10 a_0_24… lm_1    0.160         0.138   0.00507     7.41   0.00964     1   83.4
## # ℹ 246 more rows
## # ℹ 6 more variables: AIC <dbl>, BIC <dbl>, deviance <dbl>, df.residual <int>,
## #   nobs <int>, poly <dbl>

Selecting the best fitting models.

best_weighted_model <- weighted_model_comparison %>%
    dplyr::group_by(id) %>%
    dplyr::arrange(desc(AIC)) %>%
    dplyr::slice(1) %>%
    dplyr::ungroup()

total_fish <- nrow(best_weighted_model)

weighted_model_summary <- best_weighted_model %>%
    dplyr::group_by(poly) %>%
    dplyr::reframe(n = length(id), percent = round((n/total_fish) * 100, 2))

weighted_model_summary

## # A tibble: 4 × 3
##    poly     n percent
##   <dbl> <int>   <dbl>
## 1     0    38   59.4 
## 2     1     6    9.38
## 3     2     1    1.56
## 4     3    19   29.7

Visualising the regressions

ids <- labchart_tidy_fish %>% 
  dplyr::distinct(id) %>% 
  pull(id) %>% 
  as.list()

for (id_i in ids) {
  
  df_i <- labchart_tidy_fish %>%
     dplyr::filter(id == id_i) %>%
     dplyr::mutate(
      o2_bin = cut(o2, breaks = 10),  # Divide O2 into 10 bins
      bin_freq = dplyr::n(),          # Count points in each bin
      weight = 1 / bin_freq           # Weight = inverse frequency
      )
  
  best_weighted_model_i <- best_weighted_model %>% 
    dplyr::filter(id == id_i)
  
  poly_i <- best_weighted_model_i %>% 
    dplyr::pull(poly)
  
  poly_i_name <- best_weighted_model_i %>%
    dplyr::mutate(name = case_when(
      poly == 0 ~ "0th-order polynomial",
      poly == 1 ~ "1st-order polynomial",
      poly == 2 ~ "2nd-order polynomial",
      poly == 3 ~ "3rd-order polynomial",
      TRUE ~ "ERROR"
    )) %>% 
    dplyr::pull(name)
  
  r <- best_weighted_model_i %>%
    dplyr::pull(r.squared) %>% 
    round(., 2)
  
  sigma <- best_weighted_model_i %>% 
    dplyr::pull(sigma) %>% 
    round(., 2)
  
  mean_MO2 <- df_i %>% 
    dplyr::reframe(mean = mean(MO2), na.rm = TRUE) %>% 
    dplyr::pull(mean)
  
   x_max <- df_i %>%
    dplyr::reframe(max = max(o2), na.rm = TRUE) %>% 
    dplyr::pull(max)
   
   y_max <- df_i %>%
    dplyr::reframe(max = max(MO2), na.rm = TRUE) %>% 
    dplyr::pull(max)
   
  plot <- df_i %>% 
    ggplot(aes(x = o2, y = MO2, weight = weight)) +
    geom_point() +
    geom_smooth(method = "lm", formula = y ~ poly(x, poly_i), se = FALSE, colour = "blue") +
    geom_hline(yintercept = mean_MO2, colour = "grey", linetype = "dashed", linewidth = 1) + 
    annotate("text", x = x_max/2, 
             y = y_max, 
             label = paste0(poly_i_name, "\n", "R = ", r, " Sigma = ", sigma), 
             hjust = 0, vjust = 1, size = 4) +
    labs(
    title = paste0(id_i),
    x = "O2 (mg/L)",
    y = "MO2 (mg O2 g/h)"
    ) +
    theme_minimal()
  
  print(plot)
}

model_summary <- bind_rows(model_summary, weighted_model_summary)

Pcrit Chabot method

Here we will calculate Pcrit using Chabot method and function calcO2crit. We are using our estimates for SMR (mean of lowest three).

This function uses the fifth percentile of the MO2 values observed at dissolved oxygen levels ≥ 80% air saturation as the criterion to assess low MO2 values. The algorithm then identifies all the MO2 measurements greater than this minimally acceptable MO2 value. Within this sub-set, it identifies the ̇ MO2 measurement made at the lowest DO and thereafter considers this DO as candidate for breakpoint (named pivotDO in the script). A regression is then calculated using observations at DO levels < pivotDO, and a first estimate of O2crit is calculated as the intersection of this regression line with the horizontal line representing SMR. The script then goes through validation steps to ensure that the slope of the regression is not so low that the line, projected to normoxic DO levels, passes below any MO2 values observed in normoxia. It also ensures that the intercept is not greater than zero. Corrective measures are taken if such problems are encountered.

lowestMO2 default is the quantile(Data\(MO2[Data\)DO >= 80], p=0.05). It is used to segment the data and locate the pivotDO.

ids <- labchart_tidy_fish %>%
    dplyr::distinct(id) %>%
    dplyr::pull()

pcrit_model_df_list <- list()
pcrit_models <- list()

for (id_i in ids) {

    df_i <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i)

    o2crit <- calcO2crit(Data = df_i, SMR = df_i$SMR[1], lowestMO2 = NA, gapLimit = 4,
        max.nb.MO2.for.reg = 7)

    vaule <- o2crit$o2crit
    lowestMO2 = quantile(df_i$MO2[df_i$DO >= 80], p = 0.05)
    SMR <- o2crit$SMR
    nb_mo2_conforming <- o2crit$Nb_MO2_conforming
    r2 <- o2crit$r2
    method <- o2crit$Method
    p <- o2crit$P[1]

    pcrit_model_df <- tibble(id = id_i, pcrit_vaule = vaule, pcrit_smr = SMR, pcrit_lowestMO2 = lowestMO2,
        pcrit_nb_mo2_conforming = nb_mo2_conforming, pcrit_r2 = r2, pcrit_method = method,
        pcrit_p = p)

    pcrit_model_df_list[[id_i]] <- pcrit_model_df

    pcrit_models[[id_i]] <- o2crit

}

pcrit_model_df <- bind_rows(pcrit_model_df_list)

Ploting Pcrit

Here’s the plots for the Pcrit estimates

# Create output directory if needed
output_fig_pcrit_chabot_wd <- file.path(output_fig_wd, "model_chabot")
if (!dir.exists(output_fig_pcrit_chabot_wd)) {
    dir.create(output_fig_pcrit_chabot_wd)
}

ids <- labchart_tidy_fish %>%
    dplyr::distinct(id) %>%
    dplyr::pull()

pcrit_chabot_list <- list()

# Open a single PDF device
pdf(file = file.path(output_fig_pcrit_chabot_wd, "combined_chabot_plots.pdf"), width = 8,
    height = 6)

for (id_i in ids) {

    r2 <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_r2 = round(pcrit_r2, 3)) %>%
        dplyr::pull(pcrit_r2)

    conforming <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_nb_mo2_conforming = round(pcrit_nb_mo2_conforming, 3)) %>%
        dplyr::pull(pcrit_nb_mo2_conforming)

    P <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_p = round(pcrit_p, 3)) %>%
        dplyr::pull(pcrit_p)

    SMR <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_smr = round(pcrit_smr, 3)) %>%
        dplyr::pull(pcrit_smr)

    lowestMO2 <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_lowestMO2 = round(pcrit_lowestMO2, 3)) %>%
        dplyr::pull(pcrit_lowestMO2)

    # Generate and render the plot
    plotO2crit(o2critobj = pcrit_models[[id_i]])

    # Add a title
    mtext(text = paste0(id_i), side = 3, line = 2, adj = 0, col = "blue", font = 2,
        cex = 1.2)

    mtext(text = paste0("R2 = ", r2, "; p = ", P, "; CP < SMR = ", conforming, "; SMR = ",
        SMR, "; lowestMO2 = ", lowestMO2), side = 3, line = 1, adj = 0, col = "blue",
        font = 1, cex = 0.8)
}

# Close the PDF device *after* the loop
dev.off()

## png 
##   2

Printing in htlm document

ids <- labchart_tidy_fish %>%
    dplyr::distinct(id) %>%
    dplyr::pull()

for (id_i in ids) {

    comment <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i) %>%
        dplyr::slice(1) %>%
        dplyr::mutate(comment = if_else(is.na(comments), "", paste0("#", comments))) %>%
        pull(comment)

    r2 <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_r2 = round(pcrit_r2, 3)) %>%
        dplyr::pull(pcrit_r2)

    conforming <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_nb_mo2_conforming = round(pcrit_nb_mo2_conforming, 3)) %>%
        dplyr::pull(pcrit_nb_mo2_conforming)

    P <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_p = round(pcrit_p, 3)) %>%
        dplyr::pull(pcrit_p)

    SMR <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_smr = round(pcrit_smr, 3)) %>%
        dplyr::pull(pcrit_smr)

    lowestMO2 <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_lowestMO2 = round(pcrit_lowestMO2, 3)) %>%
        dplyr::pull(pcrit_lowestMO2)

    # Generate and render the plot
    plotO2crit(o2critobj = pcrit_models[[id_i]])

    # Add a title
    mtext(text = paste0(id_i, " ", comment), side = 3, line = 2, adj = 0, col = "blue",
        font = 2, cex = 1.2)

    mtext(text = paste0("R2 = ", r2, "; p = ", P, "; CP < SMR = ", conforming, "; SMR = ",
        SMR, "; lowestMO2 = ", lowestMO2), side = 3, line = 1, adj = 0, col = "blue",
        font = 1, cex = 0.8)
}

Pcrit identified

We need to set some rules as to when the Pcrit estimates are reliable, as it seems many of our fish do not seem to reach a Pcrit.

We can filter for only cases were at the lowest O2 value three consecutive MO2 measures full below our SMR and fifth percentile of the MO2 values observed at dissolved O2 levels >80%. In the model output these are called nb_mo2_conforming points.

pcrit_list <- pcrit_model_df %>%
    dplyr::filter(pcrit_nb_mo2_conforming > 2) %>%
    pull(id)

mean_pcrit <- pcrit_model_df %>%
    dplyr::filter(pcrit_nb_mo2_conforming > 2) %>%
    dplyr::reframe(mean = mean(pcrit_vaule)) %>%
    pull(mean)

paste0("There are ", length(pcrit_list), " fish with identified Pcrits. ", "The mean Pcrit is ",
    round(mean_pcrit, 2))

## [1] "There are 14 fish with identified Pcrits. The mean Pcrit is 22.83"

for (id_i in pcrit_list) {

    comment <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i) %>%
        dplyr::slice(1) %>%
        dplyr::mutate(comment = if_else(is.na(comments), "", paste0("#", comments))) %>%
        pull(comment)

    r2 <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_r2 = round(pcrit_r2, 3)) %>%
        dplyr::pull(pcrit_r2)

    conforming <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_nb_mo2_conforming = round(pcrit_nb_mo2_conforming, 3)) %>%
        dplyr::pull(pcrit_nb_mo2_conforming)

    P <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_p = round(pcrit_p, 3)) %>%
        dplyr::pull(pcrit_p)

    SMR <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_smr = round(pcrit_smr, 3)) %>%
        dplyr::pull(pcrit_smr)

    lowestMO2 <- pcrit_model_df %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_lowestMO2 = round(pcrit_lowestMO2, 3)) %>%
        dplyr::pull(pcrit_lowestMO2)

    # Generate and render the plot
    plotO2crit(o2critobj = pcrit_models[[id_i]])

    # Add a title
    mtext(text = paste0(id_i, " ", comment), side = 3, line = 2, adj = 0, col = "blue",
        font = 2, cex = 1.2)

    mtext(text = paste0("R2 = ", r2, "; p = ", P, "; CP < SMR = ", conforming, "; SMR = ",
        SMR, "; lowestMO2 = ", lowestMO2), side = 3, line = 1, adj = 0, col = "blue",
        font = 1, cex = 0.8)
}

Caculating Pcrit with Chabot SMR

ids <- labchart_tidy_fish %>%
    dplyr::distinct(id) %>%
    dplyr::pull()

pcrit_model_df_list_2 <- list()
pcrit_models_2 <- list()

for (id_i in ids) {

    df_i <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i)

    o2crit <- calcO2crit(Data = df_i, SMR = df_i$SMR_CHABOT[1], lowestMO2 = NA, gapLimit = 4,
        max.nb.MO2.for.reg = 7)

    lowestMO2 = quantile(df_i$MO2[df_i$DO >= 80], p = 0.05)
    vaule <- o2crit$o2crit
    SMR <- o2crit$SMR
    nb_mo2_conforming <- o2crit$Nb_MO2_conforming
    r2 <- o2crit$r2
    method <- o2crit$Method
    p <- o2crit$P[1]

    pcrit_model_df <- tibble(id = id_i, pcrit_vaule = vaule, pcrit_SMR = SMR, pcrit_lowestMO2 = lowestMO2,
        pcrit_nb_mo2_conforming = nb_mo2_conforming, pcrit_r2 = r2, pcrit_method = method,
        pcrit_p = p)

    pcrit_model_df_list_2[[id_i]] <- pcrit_model_df

    pcrit_models_2[[id_i]] <- o2crit

}

pcrit_model_df_2 <- bind_rows(pcrit_model_df_list_2)

Plotting with the SMR Chabot method

ids <- labchart_tidy_fish %>%
    dplyr::distinct(id) %>%
    dplyr::pull()

for (id_i in ids) {

    comment <- labchart_tidy_fish %>%
        dplyr::filter(id == id_i) %>%
        dplyr::slice(1) %>%
        dplyr::mutate(comment = if_else(is.na(comments), "", paste0("#", comments))) %>%
        pull(comment)

    r2 <- pcrit_model_df_2 %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_r2 = round(pcrit_r2, 3)) %>%
        dplyr::pull(pcrit_r2)

    conforming <- pcrit_model_df_2 %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_nb_mo2_conforming = round(pcrit_nb_mo2_conforming, 3)) %>%
        dplyr::pull(pcrit_nb_mo2_conforming)

    P <- pcrit_model_df_2 %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_p = round(pcrit_p, 3)) %>%
        dplyr::pull(pcrit_p)

    SMR <- pcrit_model_df_2 %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_SMR = round(pcrit_SMR, 3)) %>%
        dplyr::pull(pcrit_SMR)

    lowestMO2 <- pcrit_model_df_2 %>%
        dplyr::filter(id == id_i) %>%
        dplyr::mutate(pcrit_lowestMO2 = round(pcrit_lowestMO2, 3)) %>%
        dplyr::pull(pcrit_lowestMO2)

    # Generate and render the plot
    plotO2crit(o2critobj = pcrit_models_2[[id_i]])

    # Add a title
    mtext(text = paste0(id_i, " ", comment), side = 3, line = 2, adj = 0, col = "blue",
        font = 2, cex = 1.2)

    mtext(text = paste0("R2 = ", r2, "; p = ", P, "; CP < SMR = ", conforming, "; SMR = ",
        SMR, "; lowestMO2 = ", lowestMO2), side = 3, line = 1, adj = 0, col = "blue",
        font = 1, cex = 0.8)
}

Other techniques for Pcrit calculation

Here using the 100 closed trials we will estimate Pcrit with five popular techniques for Pcrit calculation: the traditional breakpoint metric (broken stick regression), the nonlinear regression metric (Marshall et al. 2013), the sub-prediction interval metric (Birk et al. 2019), the alpha-based Pcrit method (Seibel et al. 2021), and the linear low O2 (LLO) method (Reemeyer & Rees 2019).

The function is called calc_pcrit() and is part of the respirometry package.

Link: https://search.r-project.org/CRAN/refmans/respirometry/html/calc_pcrit.html

Model parameters

Parameters to consider

• avg_top_n: for alpha method, a numeric value representing the number of top α0 (MO2/PO2) values to average together to estimate α. Default is 1. We recommend no more than 3 to avoid diminishing the α value with sub-maximal observations.
  

• level: for Sub_PI method, Percentage at which the prediction interval should be constructed.
  

• iqr: Only for Sub_PI. Removes mo2 observations that are this many interquartile ranges away from the mean value for the oxyregulating portion of the trial. If this filtering is not desired, set to infinity.
  

• NLR_m: only applies to NLR. Pcrit is defined as the PO2 at which the slope of the best fitting function equals NLR_m (after the MO2 data are normalized to the 90% quantile). Default is 0.065
  

• MR: A numeric value for the metabolic rate at which pcrit_alpha and pcrit_LLO should be returned. If not supplied by the user, then the mean MO2 of the “oxyregulating” portion of the curve is applied for pcrit_alpha and NA is returned for pcrit_LLO.
  

• mo2_threshold: A single numeric value above which mo2 values are ignored for alpha Pcrit estimation. Useful to removing obviously erroneous values. Default is Inf.

Formate data

We will only use 100 c trails for this.

# labchart_tidy_fish_100c <- labchart_tidy_fish %>% dplyr::filter(phase ==
# '100c') labchart_tidy_fish_100c_n <- labchart_tidy_fish_100c %>%
# dplyr::distinct(id) %>% nrow(.)  paste0('n for 100 closed = ',
# labchart_tidy_fish_100c_n)

Here we build the models

# combined_pcirt_list <- list() ids <- labchart_tidy_fish_100c %>%
# dplyr::distinct(id) %>% pull(id) %>% as.list() for (id_i in ids) { id_name <-
# id_i mo2_data <- labchart_tidy_fish_100c %>% dplyr::filter(id == id_i) MR_set
# <- mo2_data$SMR[1] %>% as.numeric() # Use tryCatch to handle errors and skip
# problematic calculations pcrit_df <- tryCatch({ pcrit_df <- calc_pcrit(po2 =
# mo2_data$o2, mo2 = mo2_data$MO2, method = 'All', avg_top_n = 2, # alpha
# metric (default = 1) recommend no more than 3 level = 0.95, # Sub_PI metric
# (default = 0.95) iqr = 1.5, # Sub_PI metric (default = 1.5) NLR_m = 0.065, #
# NLR metric (default = 0.065) MR = MR_set, # alpha and LLO metrics,
# mo2_threshold = Inf, # alpha metric return_models = FALSE # return model
# parameters?  ) %>% as.data.frame() %>% rownames_as_column(var = 'method') %>%
# rename(value = '.') %>% tidyr::pivot_wider(., names_from = method,
# values_from = value) %>% dplyr::mutate(id = id_name) %>% dplyr::select(id,
# everything()) }, error = function(e) { message('Skipping channel ', id_name,
# ' due to error: ', conditionMessage(e)) NULL }) # Only add to list if
# pcrit_df is not NULL if (!is.null(pcrit_df)) { combined_pcirt_list[[id_name]]
# <- pcrit_df } }

Combined all the Pcrit model estimates together

# pcirt <- bind_rows(combined_pcirt_list)

Plotting Pcrit

Here we will save the plots for the various Pcrit curves.

# # Create output directory if needed output_fig_pcrit_100c_wd <-
# file.path(output_fig_wd, 'pcrit-100c') if
# (!dir.exists(output_fig_pcrit_100c_wd)) {
# dir.create(output_fig_pcrit_100c_wd) } ids <- labchart_tidy_fish_100c %>%
# dplyr::distinct(id) %>% pull(id) %>% as.list() # Open a single PDF device
# once pdf(file = file.path(output_fig_pcrit_100c_wd,
# 'combined_pcrit_plots.pdf'), width = 8, height = 6) for (id_i in ids) {
# id_name <- id_i mo2_data <- labchart_tidy_fish_100c %>% dplyr::filter(id ==
# id_i) MR_set <- mo2_data$SMR[1] %>% as.numeric() tryCatch({ # Generate and
# render the plot plot_pcrit( po2 = mo2_data$o2, mo2 = mo2_data$MO2, method =
# 'All', avg_top_n = 1, level = 0.95, iqr = 1.5, NLR_m = 0.065, MR = MR_set,
# mo2_threshold = Inf, return_models = FALSE, showNLRs = FALSE ) # Add a title
# in the top-left corner mtext(text = paste(id_name), side = 3, line = 2, adj =
# 0, # Top margin, aligned to left col = 'blue', font = 2, cex = 1.2) }, error
# = function(e) { message('Skipping channel ', id_name, ' due to error: ',
# conditionMessage(e)) }) } # Close the PDF device *after* the loop dev.off()

Plotting in the html. None of the models appear to estimate a Pcrit value convincingly.

# ids <- labchart_tidy_fish_100c %>% dplyr::distinct(id) %>% pull(id) %>%
# as.list() for (id_i in ids) { id_name <- id_i mo2_data <-
# labchart_tidy_fish_100c %>% dplyr::filter(id == id_i) MR_set <-
# mo2_data$SMR[1] %>% as.numeric() tryCatch({ # Generate and render the plot
# plot_pcrit( po2 = mo2_data$DO, mo2 = mo2_data$MO2, method = 'All', avg_top_n
# = 1, level = 0.95, iqr = 1.5, NLR_m = 0.065, MR = MR_set, mo2_threshold =
# Inf, return_models = FALSE, showNLRs = FALSE ) # Add a title in the top-left
# corner mtext(text = paste(id_name), side = 3, line = 2, adj = 0, # Top
# margin, aligned to left col = 'blue', font = 2, cex = 1.2) }, error =
# function(e) { message('Skipping channel ', id_name, ' due to error: ',
# conditionMessage(e)) }) }